2022 China Math Competition - Sum of Infinite Geometric Sequence

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A few facts in solving this problem:

1) For the sum of an infinite geometric sequence to converge, the absolute value of the common ratio must be smaller than 1.
2) If the common ratio of a geometric sequence is r, then the ratio of the sequence of the absolute values would be |r|.
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could you explain one again how did you deduce that r<0

OmPrakash-pcec